Download Lesson 8.2

Section 8.2
Geometric Distributions
AP Statistics
The Geometric Setting
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Each observation falls into one of just
two categories, which for convenience
we call “success” or “failure”
You keep trying until get a success
The observations are all independent.
The probability of success, call it p, is the
same for each observation.
AP Statistics, Section 8.2.2
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Calculating Probabilities
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The probability of rolling a 6=
The probability of rolling the first 6 on the first
roll:
The probability of rolling the first 6 after the first
roll:
AP Statistics, Section 8.2.2
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Calculating Probabilities
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The probability of rolling a 6=1/6
The probability of rolling the first 6 on the second
roll:
The probability of rolling the first 6 on the second
roll or before:
AP Statistics, Section 8.2.2
4
Calculating Probabilities
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The probability of rolling a 6=1/6
The probability of rolling the first 6 after the second
roll:
AP Statistics, Section 8.2.2
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You can use these formulas
n 1
P( X  n)  pq , geometpdf(p,n)
P( X  n)  1  p  , 1-geometcdf(p,n)
n
P( X  n)  1  1  p  , geometcdf(p,n)
n
AP Statistics, Section 8.2.2
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Formulas for Geometric Distribution
1
X 
p
1 p
1 p
  2 , X 
2
p
p
2
X
AP Statistics, Section 8.2.2
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
In New York City at rush hour, the chance
that a taxicab passes someone and is
available is 15%.
 a)
How many cabs can you expect to pass
you for you to find one that is free
 b)
what is the probability that more than 10
cabs pass you before you find one that is free.
Examples
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You are a barista at Starbucks. The probability that a customer orders a "Holiday
Drink" is 0.7. Assume that drink orders are independent. Find the following
probabilities:
What is the probability that 5 of the next 10 customers order a holiday drink?
What is the probability that it takes fewer than 3 customers before someone orders
the first holiday drink?
What is the probability that at least 6 of the next 10 customers order a holiday drink?
How many customers out of the next 10 customers would you expect to order a
holiday drink?
How many customers do you expect to order before you get your first holiday drink
order?
What is the probability that 5 customers order before someone orders a holiday
drink?
AP Statistics, Section 8.2.2
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